On certain bounds for the divisor function

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 2, Pages 410–417
DOI: 10.7546/nntdm.2024.30.2.410-417
Full paper (PDF, 222 Kb)

Details

Authors and affiliations

József Sándor
Department of Mathematics, Babeș-Bolyai University
4000840 Cluj-Napoca, Romania

Abstract

We offer various bounds for the divisor function , in terms of , or other arithmetical functions.

Keywords

• Divisor functions
• Arithmetic functions
• Inequalities for arithmetic functions
• Inequalities for sums

2020 Mathematics Subject Classification

• 11A25
• 26D15

References

1. Cârtoaje, V. (2007). The equal variable method. Journal of Inequalities in Pure and Applied Mathematics, 8(1), Article 15.
2. Faiziev, R. F. (1989). A series of new general inequalities and identities. Doklady Akademii Nauk Tadzhikskoĭ SSR, 32(9), 577–581 (in Russian).
   
3. Sándor, J. (2009). A better lower bound for σk(n). Octogon Mathematical Magazine, 17(2), 767–768.
4. Sándor, J. (2010). Two arithmetic inequalities. Advanced Studies in Contemporary Mathematics, 20(2), 197–202.
5. Sándor, J. (2012). On an inequality between means of n arguments. Octogon Mathematical Magazine, 20(1), 246–249.
6. Sándor, J., & Atanassov, K. T. (2021). Arithmetic Functions. Nova Science Publishing.
7. Sándor, J., & Kóvacs, L. (2009). An inequality for the number of divisors of n. Octogon Mathematical Magazine, 17(2), 746–750.
8. Sándor, J., Mitrinović, D. S., & Crstici, B. (2006). Handbook of Number Theory I. Springer

Manuscript history

• Received: 10 February 2024
• Revised: 20 May 2024
• Accepted: 29 May 2024
• Online First: 30 May 2024

Copyright information

Ⓒ 2024 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).